Homogeneous Geodesics of $4$-dimensional Solvable Lie Groups

Abstract

We study homogeneous geodesics in $4$-dimensional solvable Lie groups $\mathrm{Sol}_0^4$, 
 $\mathrm{Sol}_1^4$, $\mathrm{Sol}_{m,n}$ and $\mathrm{Nil}_4$.